PRP Records

Probable Primes Top 10000

(173006 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
60012^231016-11052369543Enzo Doria05/2014
60022^231014+57729457569543Lelio R Paula02/2016
600314^60658+6769522Lelio R Paula09/2013
60045^99418+3669491Lelio R Paula06/2013
60057^82203-3069470Lelio R Paula09/2013
60065^99359-2^9936069449Mike Oakes12/2010
6007(29*2^230684+1)/139569442Lelio R Paula08/2012
6008(19*10^69424+77)/369425Robert Price08/2016
600919^54287-9669420Lelio R Paula09/2013
60102^230541+5890569400Lelio R Paula04/2012
60112^230506+1270569390Lelio R Paula02/2013
60128*6^89156-569378Lelio R Paula09/2014
60132^230438-11134769369Enzo Doria05/2014
60142^230428-9969366Lelio R Paula02/2012
60153*10^69354+1769355Robert Price03/2017
6016(493*10^69340-7)/969342Robert Price07/2016
6017(41*10^69321+373)/969322Robert Price04/2017
60186^89072+5369312Lelio R Paula09/2013
6019155^31639+269300Lelio R Paula05/2013
60203*7^81965-469269Lelio R Paula09/2014
6021(86*10^69260-77)/969261Robert Price05/2016
60229*5^99087+469260Lelio R Paula09/2014
60233^145145+266069252Lelio R Paula09/2013
602511^66492-114069245Enzo Doria11/2012
60245*3^145129-469245Lelio R Paula04/2014
60267*3^145126+869244Lelio R Paula04/2014
602711^66480-237069232Enzo Doria12/2012
60282^229962-6569226Lelio R Paula02/2012
60292^229958-11073369225Enzo Doria05/2014
6030V(332407)69225Serge Batalov03/2015
60316^88959+769224Lelio R Paula09/2013
603215^58855-9469219Lelio R Paula09/2013
6033(2^229838+47)/1208169185Lelio R Paula04/2012
60343^144952+9869160Lelio R Paula09/2013
60355^98941-7269157Lelio R Paula06/2013
6036(17*2^229604-1)/22969117Lelio R Paula01/2014
60372^229585-106369112Yves Minet11/2012
6038(13*2^229567-1)/1969107Lelio R Paula01/2014
6039(13*2^229393-1)/569055Lelio R Paula01/2014
6040(53*10^69050-17)/969051Robert Price09/2015
60412^229305-186853369028Enzo Doria04/2016
60422^229297+138569026Lelio R Paula04/2012
604318^54986-244169023Enzo Doria03/2013
6044(34*10^69021-7)/9/3/6769020Makoto Morimoto04/2016
60455^98736-1463669014Enzo Doria02/2013
6046(13^61949-5^61949)/869007Robert Price03/2013
6047(2^229227+5)/61169002Lelio R Paula04/2012
60482^229216-11327969001Enzo Doria07/2014
604910^68994+5191368995Patrick De Geest03/2016
605110^68994-10^5814-168994Serge Batalov01/2011
605010^68994-8294768994Patrick De Geest03/2016
6052(17*2^229136-1)/238168975Lelio R Paula01/2014
60532^229113+10768970Lelio R Paula02/2012
605411^66202-441068943Enzo Doria01/2013
605512^63883+568942Lelio R Paula07/2013
6056(9913*2^229002-1)/39990368935Lelio R Paula04/2015
60572^228962-11158168925Enzo Doria05/2014
60582^228944+8168920Henri Lifchitz01/2007
605911^66174-5468914Lelio R Paula09/2013
60602^228913-11126568910Enzo Doria05/2014
60612^228902+7351968907Enzo Doria04/2016
6062(47*2^228884+1)/6368901Lelio R Paula04/2015
60632^228821+7642768882Enzo Doria05/2016
60643^144340+5068868Lelio R Paula09/2013
60652^228758-11296768864Enzo Doria06/2014
60662^228743-11137968859Enzo Doria05/2014
60672^228741-11091168858Enzo Doria05/2014
6069lucasU(1926,1,20964)-lucasU(1926,1,20963)68857Mike Oakes05/2009
60683*5^98511-868857Lelio R Paula09/2014
60702^228717+46768851Lelio R Paula02/2011
6071Phi(153218,10)/2211855049/23592660859/49771411729168849Maksym Voznyy10/2011
6072(509203*2^228665-1)/3568840Lelio R Paula04/2015
60738^76213-7^7621368828Ananda Tallur & Jean-Louis Charton11/2003
607411^66074-105068809Enzo Doria11/2012
60752^228484+18168781Lelio R Paula02/2012
60762^228479-5869568780Lelio R Paula04/2012
60772^228465-1585368775Enzo Doria04/2013
607811^66040-540068774Enzo Doria01/2013
6079(13*2^228441-1)/57568766Lelio R Paula01/2014
6080(17*2^228393+1)/29568752Lelio R Paula08/2012
60812*10^68744+4168745Robert Price01/2017
608211^66011-15068744Enzo Doria08/2012
6083(13*2^228304-1)/8168726Lelio R Paula01/2014
60842^228295-11107968724Enzo Doria05/2014
6085(3^144039+7)/2268723Lelio R Paula04/2012
6086(8*10^68722+49)/368723Robert Price03/2016
6087(35*10^68718+1)/968719Serge Batalov11/2010
60882^228271-22827168717Henri Lifchitz11/2004
60892^228257+8287568713Lelio R Paula02/2013
60903^144013+4068712Lelio R Paula09/2013
609113^61671-8668699Lelio R Paula09/2013
609217^55828-7268694Lelio R Paula09/2013
60936^88259+6168679Lelio R Paula09/2013
609418^54699-568663Lelio R Paula09/2013
609533^45216+268662Lelio R Paula05/2013
6096(2^228073-5)/368657Lelio R Paula04/2012
6097(2^(6*38012+1)-5)/368657Kevin Acres11/2013
60982^228055-11160768652Enzo Doria05/2014
60992^228054-11476168652Enzo Doria05/2015
61002^228041+118568648Lelio R Paula04/2012
61012^228040-103768647Yves Minet11/2012
61022*F(328450)-168642Henri Lifchitz12/2009
61035^98201-3468640Lelio R Paula06/2013
61049^71910+3*8^71910-2*4^71910-3*2^7191068620Mike Oakes12/2010
61057*2^227780-368570Lelio R Paula04/2014
61062^227733-12168555Lelio R Paula02/2012
61072^227702-1696768546Enzo Doria05/2013
61082^227689-11165568542Enzo Doria05/2014
6109gcd(V(823915),5*F(164783)*(F(164783)-1)+1)68536Serge Batalov04/2015
61105^98051+268535Ray Chandler07/2011
61115*10^68524+5168525Robert Price01/2017
6112(11*10^68520-149)/368521Robert Price01/2017
611319^53573-7868507Lelio R Paula09/2013
6114(68*10^68504+13)/968505Ray Chandler10/2010
61159*5^98003+468503Lelio R Paula09/2014
61162^227528+5168493Lelio R Paula02/2012
61173^143497+868466Lelio R Paula04/2012
61182^227430-9568464Lelio R Paula02/2012
61193*5^97934-268454Lelio R Paula09/2014
612020^52613+7768452Lelio R Paula09/2013
61212^227371+3276968446Lelio R Paula04/2012
6122(3^143465+4)/2127042006768440Lelio R Paula04/2012
6123CopelandErdos(68433)68433Eric W. Weisstein08/2013
61242^227323+7543168432Enzo Doria04/2016
61252^227314-196568429Lelio R Paula04/2012
61262^227303-11061768426Enzo Doria05/2014
61287^80963+6668422Lelio R Paula07/2013
61272^227290+7384968422Enzo Doria04/2016
6129(14^59693-1)/1368415Paul Bourdelais06/2008
61302^227256-278624968411Enzo Doria03/2016
61328*10^68400-768401Dmitry Domanov11/2010
6131(15*2^227228-1)/58368401Lelio R Paula01/2014
61332^227210+186916968398Enzo Doria05/2016
61342^227159-183863568382Enzo Doria05/2015
61352^227115-780768369Lelio R Paula10/2009
61362^227078-4735568358Lelio R Paula04/2012
6137(2^227063-1017)/34968351Lelio R Paula04/2012
61382^227057+14809168351Lelio R Paula04/2012
61392^227046+18768348Lelio R Paula02/2012
614011^65608-72068324Enzo Doria11/2012
614133408!2-2^33408-168315Joe McLean05/2017
61422^226894-12368302Lelio R Paula02/2012
614310^68297+14155968298Patrick De Geest05/2013
614410^68297-9368297Robert Price05/2011
6145680^24107-679^2410768284Jean-Louis Charton07/2010
614612^63267+5968277Lelio R Paula07/2013
61472^226785-115968270Yves Minet11/2012
61487^80769+9068258Lelio R Paula07/2013
61492^226741+6658768256Yves Minet10/2010
61502^226720-11240368250Enzo Doria06/2014
6151(78557*2^226694+1)/368247Lelio R Paula06/2014
6152(83*10^68231+7)/968232Robert Price10/2015
615365^37636+1668231Lelio R Paula01/2016
61545^97615-4^(97615+1)68230Robert Price04/2016
615512^63200-4368205Lelio R Paula07/2013
6156-330*Bern(21940)/22379062073368201Serge Batalov04/2015
61573^142925+868068193Lelio R Paula06/2013
61583*2^226512-768188Lelio R Paula04/2014
615914^59484+5768177Lelio R Paula08/2013
616011^65438-219068147Enzo Doria12/2012
616191^34784-268144Lelio R Paula09/2013
6162(2^226336-3)*6-768135Gilbert Mozzo06/2016
6163(22*10^68133-37)/368134Robert Price05/2017
61645^97476+3668133Lelio R Paula06/2013
61653*5^97474-268132Lelio R Paula09/2014
616612^63130+4968129Lelio R Paula07/2013
61672^226281+538568118Lelio R Paula04/2012
61682^226257-304968111Yves Minet10/2014
6169(28*10^68107-43)/368108Robert Price04/2016
61702^226243-258768106Yves Minet07/2014
617120^52346-1168104Lelio R Paula09/2013
61722^226205-9968095Lelio R Paula02/2012
61732^226187-4968090Lelio R Paula02/2012
61743^142708+7668090Lelio R Paula06/2013
61757*10^68088-8968089Robert Price01/2017
61762^226154+7183968080Enzo Doria04/2016
6177(10^68078+59)/368078Serge Batalov12/2014
617914^59387+6968066Lelio R Paula08/2013
61782^226108-11342968066Enzo Doria07/2014
6180(24^49307-1)/2368053Robert Price04/2012
618115^57859-2868048Lelio R Paula08/2013
6182(509203*2^226003-1)/1368039Lelio R Paula04/2015
61832^226015-11136168038Enzo Doria05/2014
6184156*(10^(4*17000)-1)/101-168001Robert Price05/2014
61852^225878-101767997Lelio R Paula04/2012
61863*8^75289+5^75289-3*4^75289+3*2^7528967994Mike Oakes11/2010
61873*2^225865+567993Lelio R Paula04/2014
618811^65284-582067987Enzo Doria01/2013
618919^53166+7067987Lelio R Paula08/2013
61902^225837+7540767984Enzo Doria04/2016
61913^142464-11265467973Enzo Doria06/2014
61922^225777+9567966Lelio R Paula02/2012
6193(2^225641-1017)/13881567920Lelio R Paula04/2012
61942^225609-1844567916Enzo Doria05/2013
61952^225542-17767895Lelio R Paula02/2012
61962^225536-2967894Henri Lifchitz05/2005
619711^65190-339067889Enzo Doria12/2012
61983^142249-2^(142249-1)67871Robert Price01/2016
619911^65168-483067866Enzo Doria01/2013
620010^67863+5862767864Patrick De Geest01/2016
620110^67863-1167863Robert Price05/2011
6202(1!)^2+(2!)^2+(3!)^2+...+(9566!)^267856T. D. Noe02/2006
6203(19*2^225357-1)/1167840Lelio R Paula01/2014
62049*6^87164-767828Lelio R Paula09/2014
6205131^32034+13067825Norbert Schneider03/2015
6206(29*2^225314+1)/1088167824Lelio R Paula08/2012
6207(134*10^67816+7)/367818Robert Price02/2017
62082^225261+85567811Lelio R Paula04/2012
6209(29*2^225252-1)/293367806Lelio R Paula01/2014
6210(4*10^67796+23)/967796Robert Price11/2014
6211(23*2^225177+1)/3167785Lelio R Paula08/2012
6212(4*10^67784+149)/967784Robert Price03/2017
62132^225120+15167768Lelio R Paula02/2012
6214(44^41233+1)/4567763Robert Price11/2013
62158*10^67742+967743Dmitry Domanov11/2010
62162^224977+108967725Lelio R Paula04/2012
6217(2^224950+5)/1950967713Lelio R Paula04/2012
621811^65011-597067702Enzo Doria01/2013
621988*10^67691+767693Robert Price11/2016
622011^65000-714067691Enzo Doria01/2013
62212^224841+5967684Lelio R Paula02/2012
622233129!2+2^3312967684Robert Price09/2015
62232^224827+841567680Lelio R Paula02/2013
6224(9913*2^224821-1)/1982567678Lelio R Paula04/2015
62252^224815-4978967677Henri Lifchitz04/2005
6226(43*10^67664+11)/967665Robert Price06/2015
6227(292*10^67659-1)/367661Robert Price01/2017
6228(17*2^224766+1)/2900767659Lelio R Paula06/2012
62292^224744+57729457567655Lelio R Paula02/2016
6230((1+sqrt(7)+sqrt(6))^45863-1)*((1+sqrt(7)-sqrt(6))^45863-1)*((1-sqrt(7)+sqrt(6))^45863-1)*((1-sqrt(767653Mike Oakes05/2009
6231(2^224721+78557)/173967645Lelio R Paula05/2012
62322^224700+191567642Lelio R Paula04/2012
6233(29*2^224694-1)/19890567636Lelio R Paula01/2014
62342^224658-9367629Lelio R Paula02/2012
62352^224624-1307767619Enzo Doria10/2012
623618^53860-331967609Enzo Doria03/2013
6237(21181*2^224570+1)/567606Lelio R Paula06/2014
62382^224578-11104167605Enzo Doria05/2014
62392^224569-11323367603Enzo Doria07/2014
62402^224562-11317167600Enzo Doria07/2014
62412^224556-11312967599Enzo Doria07/2014
62426*7^79980-567592Lelio R Paula09/2014
6243(6883*2^224523-1)/1603167588Lelio R Paula04/2015
6244(52*10^67578-61)/967579Robert Price09/2015
6245(17^54919-1)/1667574Paul Bourdelais03/2010
6246(2^224363-9)/195167537Lelio R Paula04/2012
624747719!3-5904967516Robert Price12/2015
6248(22^50287+1)/2367506Robert Price06/2013
624911^64811-582067494Enzo Doria01/2013
6250131^31870+31870^13167478Serge Batalov05/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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